Calcudoku Online
Fill every row and column with each number exactly once while satisfying arithmetic cage clues. This is a real browser puzzle engine with independently verified unique solutions, not a static worksheet or answer page.
What is Calcudoku?
Calcudoku is a number-logic puzzle built from two kinds of constraints at once. First, the grid follows a Latin-square rule: on an N×N board, each row and each column must contain the digits 1 through N exactly once. A 4×4 puzzle therefore uses 1, 2, 3 and 4 in every row and column. A 6×6 puzzle uses 1 through 6. Unlike Sudoku, there are no 3×3 box rules.
Second, outlined cages add arithmetic clues. A cage marked 7+ must contain values that add to seven. A 12× cage must multiply to twelve. Two-cell subtraction and division cages work without a fixed order, so a 2− cage can contain 1 and 3 in either position, while a 3÷ cage can contain 2 and 6 in either position. Single-cell cages simply give that cell’s value.
The interaction between row, column and cage rules is where the puzzle becomes interesting. A cage may allow several arithmetic combinations by itself, but most disappear once you account for values already used in its rows and columns. Good solving therefore alternates between arithmetic and placement logic instead of treating them as separate tasks.
How this version avoids guesswork about puzzle quality
Randomly drawing cages around a completed Latin square is easy. Proving that the resulting clue set has only one answer is the harder part. Every bundled source in this release is checked with an independent backtracking solver that knows the row, column and cage-operation constraints. A source is accepted only when the solver counts exactly one solution. The release contains 20 verified 4×4 sources, 20 verified 5×5 sources and 20 verified 6×6 sources.
Practice can rotate or reflect a verified source in eight square-preserving ways. Those transforms move the cells and cages without changing the mathematical structure, producing 480 reproducible replay variants from the 60 verified sources. The transformation is part of the saved puzzle identity, so an autosave resumes the exact same layout.
Three useful difficulty steps
Easy 4×4 is the cleanest place to learn the mechanic. The smaller digit range keeps cage arithmetic visible and gives more immediate row or column deductions. It is suitable for learning how subtraction and division cages behave without a large search space.
Standard 5×5 increases the number of possible cage combinations and makes row/column interaction more important. This is the default Practice setting because it keeps arithmetic manageable while creating enough constraint overlap for a satisfying solve.
Hard 6×6 uses a broader 1–6 digit range and generally larger cages with fewer single-cell anchors. The arithmetic possibilities are wider, so the board rewards candidate management and repeated cross-checking between cage and Latin-square constraints.
Tools that support reasoning instead of replacing it
Notes mode lets you record candidate digits in an empty cell. Auto Notes computes candidates from the current row, column and cage constraints. The selected-cage panel lists arithmetic possibilities still compatible with your current entries. These tools expose constraints but do not place a final answer, so using them does not invalidate a clean solve.
Undo and Redo support experimentation. Check reports entered values that disagree with the frozen solution and marks the run assisted for clean-best purposes. Hint fills one cell and also makes the solve non-clean. Autosave stores values, notes, elapsed time and the exact puzzle identity locally in this browser so an interrupted Practice round can continue later.
Why arithmetic cage puzzles are useful practice
Calcudoku trains a different mixture of skills from ordinary Sudoku. The Latin-square rule rewards elimination and working memory, while the cage clues repeatedly exercise small sums, products, differences and exact division. You often need to reason about sets of values rather than calculate a single answer. For example, a two-cell 10+ cage on a 6×6 board can only be 4 and 6, while a 12× cage might have several possibilities until crossing rows or columns remove them.
The game records local completion time, clean solves and personal bests by difficulty. Those are task records from this browser, not IQ scores, classroom grades or global rankings. There is no account, backend leaderboard or claim that a fast solve measures general mathematical ability.
Daily or unlimited?
Unlimited Practice is for deliberate repetition. Choose Easy, Standard or Hard and generate a fresh seeded source/transform combination whenever you want another puzzle. Daily Calcudoku uses one date-stable verified puzzle each day and keeps its own specialist streak. It does not enter or alter the platform’s separate Today’s 6 rotation.